Question

prove that 5-√3 is an irrational

Answer 1

$\boxed{Question-}$prove that 5-√3 is an irrational

$\huge\bold{Solution}$

Let us assume that 5 - √3 is rational. Then it can be written in the form

5 - √3 = p/q

or

5 - p/q = √3

✍️It implies √3 is a rational number [Since 5 - p/q are rationals]

➡️But this $\bold{contradicts}$ to the fact that √3 is irrational.

➡️Hence our supposition was $\bold{wrong}$.

➡️ Therefore 5 - √3 is irrational.

Answer 2

Answer:

Step-by-step explanation:let us assume that 5- root3 is a rational number. So, it can be written as

5- root3=p/q ---- 1

where p and q are co primes and q is not equal to 0 (general form of a rational number)

Thus, from 1, root3=5-p/q

=root3= 5q-p/q ----2

So lhs of eq.2 isirrational whilr rhs is rational. Sp we arrive at a contradiction and oir assumptionnis wrong. Thus, 5-root 3 is an irrational number.

Hope it helps